Image perceptual similarity is a fundamental issue in image processing, image retrieval, image management, and image understanding in general (see T. Acharya and A. K. Ray, Image Processing—Principles and Applications, Wiley InterScience, 2006, hereinafter referred to as [1]; E. Chalom, E. Asa, and E. Biton, “Measuring image similarity: An overview of some useful application”, IEEE Instrumentation and Measurement Magazine, Vol. 16, No. 1, pp. 24-28, February 2013, hereinafter referred to as [2]; R. Datta, D. Joshi, J. Li, and J. Wang, “Image retrieval: Ideas, influences, and trends of the new age”, ACM Computing Surveys, Vol. 40, No. 2, Article 5, pp. 1-60, April 2008, hereinafter referred to as [3]; Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. on Image Processing, vol. 13, no. 4, pp. 600-612, April 2004, hereinafter referred to as [16]). In image processing such as image compression, image denoising, and image reconstruction, one can use a similarity metric or function to measure the perceptual similarity between the original image A and a processed image Â and evaluate the performance of the corresponding image processing system. In image retrieval and image management, one can use a proper similarity metric or function to measure the perceptual similarity between any two independent images A and B. Once such a similarity metric or function is defined for any two independent images, it could be used to retrieve images in a database which are perceptually similar to a query image according to the similarity metric or function in image retrieval, and to organize images into different groups according to their mutual similarity in image management.